Apparatus for teaching mathematics



Oct. 8, 1929. GARDNER 1,730,418

APPARATUS FOR TEACHING MATHEMATICS Filed May 31, 1927 i E m o q'q km ing a fraction.

Patented Qfct. 8 1929 I I ISABEL R. GARDNER, or BOSTON, MASSACHUSETTS AnrARA'TUs FOR T ACHING MATHEMA IOS Application filed May 31,

The principal object of my invention is to teach mathematics, particularly arithmetic, in such a way that the pupils will be interested and their mental activity increased.

5 A feature of my invention is the provision of a relatively large chart having numbers thereon readily visible to the pupils and for use with the chart a card, for example, having thereon a number,the word number includ- Another feature is the provision of another card havingthereon said number on the firstmentioned card and a listof numbers and corresponding answers the numbers appearing also on'thechart so thatthe chart and the two I 4 cards are interrelated for teaching purposes. Another feature is different sets of cards, each set consisting of a plurality of cards. One set relates toaddition, anotherto subtraction, another to multiplication, another to-division and another to fractions.

, Other features of my apparatus and method will be referred to below.

'In the drawing 1 a Figure 1 is an elevation of a chart forming part of my invention, one corner being turned back to show a portion'of the disordered numbers on the rear surface;

Figure 2 is a perspective View of a group of cards, each of which is marked with a number;

Figure 3 is a perspective view of a group of cards, each of which is marked with a fraction;

groups of cards marked with answers for addition, subtraction, multiplication, division and fractions. 1

Figure 9 is an elevation of the chart and of v a card of Figure 2 and'of a card of Figure 4; in

operative relation; and

Figure 10 is an elevation of a card of Figure 2 and a portion of the chart in operative relation.

v The chart A may be any suitable construction and may be suspended by cord B, the chart having on one face numbers from 1 to 24, forexample, all .of these numbers being shown in Figure 1 except numbers 6 to 12 which are hidden because the lower left por- D there will be another number such as the numeral 8 andso, with six cards, there will be edge a vertical and corresponding list of Figure 4 to 8 are perspective views of.

to besubtracted, forexample, from 21to give 192?. Serial Nuisaiss. I a

tion is turned back to show, that on the re- Verse faceof the chart the numbers, which may include numbers 1 to 24, are in disordered arrangement. More than24 numbers maybe usedif desired. 3

In Figure 21 show agroup of cards,-prefer ably'six, each card, such as I), having a numher on its front face, the number shown being the numeral 7. On the back face of carol available numerals 1 to 12, each face having only one numeral. g I I i In Figure 3 I Show a similar group of cards for fractions, the face of the card E having a .65 number inthe form of a fraction 1/3 and, the reverse face having a different fraction. By using 33 cards (indicated in Figure 3) and having separatenumbers on the front and rear faces Inlay have the fractions 1/12,; 2/12 and'so onup to and including 11/12; 1/11,'2/l1 andso gon up [to and including 10/11; and so on to the denominator 2, the fraction being 1/2. These cards will provide 66 fraction-numbers. v p i In Figure {L Ishow a group of cards for addition, preferably five, each card, such as F, having a number such as 7 andbelow this number a'vertical list of nu mbers towhich the indicator towbe added and at the opposite answers; For example, the answerto'7 plus 5 is 12 and the answerto? plus 14 is 21. Each card will have on its reverse face a difierent numeral number andmay have any desired list of; numbersto be added and also corresponcling answers.

preferably five, for subtraction, each card, such as G,hav ng a number such as .7 which 1s itheanswer l l.

, Figures 6 to 8 show Similar'groups Ofsinii la r cards for. multiplication, division and fractions, respectively. I a I In using my inventionthe chart A is placed so that the numerals thereon will be: clearly visible toall therpu pils and I may expose the 7 face havingthe numbers in order, or indisorder as indicated in the turned backporti'on of Figure -1, one advantage of the disordered arrangement being that the pupils can not observe from the chart itself what the answer may be, as, for example, if the problem were to add 5 to 4: the pupil might, if the numbers were in order, count down 5 numbers from 4' on the chart and find 9. This he could not do if the arrangement were disordered.

The teacher then selects a card such as D and holds it in adjacency to the chart preferably beneath the desired number. as lndicated in Figure 10, theproblem here-being to add 7 to 5. The pupils may answer orally or may write the answer. then be moved into similar adjacency to any other desired numbers; 1 Similarly for purposes of subtraction one off the cards of Figure 2'wil1 be placed in adjacency to any desired numbers on the chart, although the cardnumber should be less than the number into adjacency with which it is brought.

Similarly one of the cardsof Figure 2 will be used for problems in multiplication and division and similarly one of the cards of Figure 3 will be used for problems'in frac- 1 tions. I

It is preferable to have the size of thenumher as 7 in Figure 2, the same in height as the size of the numbers on the chart, although in i thedrawings, for economy of space, the numbers on the chart are actually smaller.

The cards shown in Figures 4 to 8 are preferably used in interrelation to the cards of Figures 2 and 3. In Figure 9 card D is so placed with relation to card F that the list of answers is hidden from the pupils and the cards D and F may be conveniently heid .5 on the chart. The pupils willthen-write the answer to the problem which is to add 7 together in this relation by a clip. 'When in such relation the card D will be placed so that its number is in adjacency to the numeral The card maybei-n movable by the teacher into adjacency to the desired number on the chart for the purpose oi'" coinputa'tion between the numbers on the chart and card. I

3. An apparatus for teaching mathematics comprising a member having a plurality of numbers, and another member having one number only, said other member being movable by the teacher into adjacency to the desired number on the first member for the purpose of computation between'the numbers on said members. I. 4. An apparatus for teaching mathematics comprising a chart having a plurality of numbers arranged in a vertical row, and a card having anumber adjacent to the top edge of the card, the depth of the card being such as to obscure several of the numbers on the chart when the top edge of the card is placed immediately below thedesired number on the chart.

5. An apparatus for teaching mathematics comprising a chart having a plurality of numbers arranged'in a row; and a card having a number adjacent to an edge of the card, the dimension of the card in the dimction-of said Tow'bei-ng such as'to obscure several of the numbers in said row when said edge is placed in adjacency to the desired visible number on the chart! 7 ISABEL "GARDNER.

- "to 5. 'The cards D and F are then moved L" so that thenumber 7 is in adj acency to the "numeral 7 on the chart and so on in accordance with the list of numbers at the left of card F, this list being for the convenience of the teacher as a record of the problems. in order and the corresponding answers on the card F being for convenience and for 'comparison with the answers of the pupils.

Any desired number on the-front or back fer anyeard of Figure Q'may be used in relaftionto thefront or back face of any card 'ot Figures 4 m 7 and the desired nunrfloerv on the front or back of any card, such as'E, Y ot Figure 3 may be usedwith acorresponding card of the group of Figure 8, such as card I claim is:

' 1. An apparatus for teaching mathematics comprising a member having one or more numbers thereon, and another 'memberhaw ing a number, said other member being mov-' 

